get angle of a line from horizon

Question

I want to know how to get an angle of a line A-B from horizontal axis X. Other questions in SO do that only between two lines. I'm aware I can always draw second line A-C and calculate but I'm wondering if there's a faster method.

EDIT: I'm very sure I'm not doing a premature optimization.

Answer 1

The x-axis is actually a line with equation

y = 0

so you could use the solution you have already.

Answer 2

You can use atan for that.

angle = atan((By-Ay)/(Bx-Ax))

Answer 3

If

1. The angle is small,
2. you can live with small inaccuracies, and
3. You can use the angle in radians and not degrees,

then there is a fast solution: Under these conditions, you can assume that tan(a) = a = atan(a), and hence just omit the atan() call.

Answer 4

You could also use arccosine, if your line is in the form [r_x,r_y], where r_x is the change in x and r_y is the change in y.

angle = arccos( r_x/( r_x*r_x + r_y*r_y ) )

---

It's slightly more opaque, but it's basically the dot product law:

angle = arccos (r . v)

Where r and v are both unit vectors (vectors of length 1). In our case, v is the vector [1,0], and r is

[r_x,r_y] / (r_x^2+r_y^2)

in order to make it a unit vector.